Stick with short answer: you could be in the doghouse there? (9)
I believe the answer is:
battersea
'you could be in the doghouse there?' is the definition.
(as in Battersea Dogs and Cats Home)
'stick with short answer' is the wordplay.
'stick' becomes 'bat' (bat is a kind of stick).
'with short' becomes 'terse' (synonyms. I am not sure about the 'with' bit.).
'answer' becomes 'a' (abbreviation eg in Q and A).
'bat'+'terse'+'a'='BATTERSEA'
Can you help me to learn more?
(Other definitions for battersea that I've seen before include "part of London" , "District of Wandsworth" , "where one may go to the dogs" , "London park" , "London district" .)